Warhammer Calculator
Advanced Math-hammer Combat Simulator & Probability Engine
0.00
Expected Hits
Expected Wounds
Unsaved Wounds
Formula: Expected Damage = Attacks × P(Hit) × P(Wound) × P(Fail Save) × Damage
Damage vs. Target Toughness (T3 to T10)
Calculated based on current Strength, AP, and Damage values.
Quick Reference Table: Armor Penetration Impact
| AP Value | Effective Save | Failed Save % | Exp. Damage (at T4) |
|---|
What is a Warhammer Calculator?
A Warhammer Calculator, often referred to by the community as a “Math-hammer” tool, is a statistical engine used to determine the average performance of units in tabletop wargaming. Whether you are playing Warhammer 40,000 or Age of Sigmar, understanding the variance of dice rolls is critical for competitive success. This Warhammer Calculator takes the guesswork out of your Command Phase and Shooting Phase by providing hard data on how many wounds you can expect to inflict on a specific target.
Players use this Warhammer Calculator to optimize their army lists, compare the efficiency of different weapon profiles, and decide whether a particular charge is worth the risk. One common misconception is that “average” means “guaranteed.” In reality, these calculations provide the mean outcome of thousands of simulated rolls, helping you play the percentages over a long tournament weekend.
Warhammer Calculator Formula and Mathematical Explanation
The math behind a Warhammer Calculator follows a series of independent binomial trials. Each stage of the attack—hitting, wounding, and saving—filters the number of potential successful outcomes.
The core formula used by our Warhammer Calculator is:
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| A (Attacks) | Total number of dice thrown | Integer | 1 – 100+ |
| P(H) | Probability of hitting based on WS/BS | Probability | 16.6% (6+) to 83.3% (2+) |
| P(W) | Probability of wounding (S vs T) | Probability | 16.6% to 83.3% |
| P(S) | Probability of the target failing their save | Probability | 0% to 100% |
| D (Damage) | Wounds lost per failed save | Integer/Dice | 1 to 6+ |
Practical Examples (Real-World Use Cases)
Example 1: Space Marine Intercessor Shooting
Using the Warhammer Calculator, let’s look at 10 shots from a Bolt Rifle (S4, AP-1, D1) hitting a Toughness 4 target with a 3+ save.
- Attacks: 10
- To Hit: 3+ (P=0.66)
- To Wound: 4+ (P=0.50)
- Save: 3+ modified to 4+ by AP-1 (P of failure = 0.50)
The Warhammer Calculator result: 10 * 0.66 * 0.50 * 0.50 * 1 = 1.65 Wounds.
Example 2: Anti-Tank Lascannon
A single Lascannon shot (S12, AP-3, D d6+1) against a Rhino (T9, 3+ save):
- Attacks: 1
- To Hit: 3+ (0.66)
- To Wound: 3+ (S12 vs T9 is 3+) (0.66)
- Save: 3+ modified to 6+ by AP-3 (P of failure = 0.833)
The Warhammer Calculator result: 1 * 0.66 * 0.66 * 0.833 * 4.5 (avg damage) = 1.66 Expected Damage.
How to Use This Warhammer Calculator
Follow these steps to maximize the utility of the Warhammer Calculator during your list-building phase:
- Step 1: Input Attack Volume: Enter the total number of attacks for the entire unit or a single model.
- Step 2: Set Hit and Wound Specs: Choose the BS/WS and input the weapon’s Strength versus the target’s Toughness.
- Step 3: Account for Defense: Select the target’s Armor Save and input the AP of your weapon. The Warhammer Calculator automatically factors in Invulnerable Saves.
- Step 4: Analyze the Results: Review the Expected Damage and the intermediate charts to see how the unit performs against varying threats.
Key Factors That Affect Warhammer Calculator Results
When using a Warhammer Calculator, several tactical factors can swing the results significantly:
- Rerolls: Rerolling 1s to hit increases efficiency by approximately 16.6%. Full rerolls are even more impactful.
- Critical Hits/Wounds: Rules like “Lethal Hits” or “Devastating Wounds” bypass specific steps of the Warhammer Calculator logic.
- Armor Penetration (AP): As shown in our table, increasing AP from 0 to -2 can double your damage against heavily armored targets.
- Invulnerable Saves: These provide a “floor” for defense, ensuring that high AP weapons aren’t too overwhelming.
- Feel No Pain (FNP): This is a secondary save layer applied after damage is determined, which reduces final expected damage by its success rate.
- Damage Variance: Weapons with D6 damage have high variance. While the Warhammer Calculator shows the mean, the “swing” can be huge in actual play.
Frequently Asked Questions (FAQ)
Does the Warhammer Calculator handle “Devastating Wounds”?
Standard versions of the Warhammer Calculator require manual adjustments for Devastating Wounds by calculating the percentage of 6s rolled to wound and adding that directly to the unsaved wound pool.
What is “Math-hammer”?
Math-hammer is the application of probability and statistics to Warhammer games. A Warhammer Calculator is the primary tool used for this practice.
Why does the calculator show decimals?
Dice are integers, but averages are not. If the Warhammer Calculator shows 2.5 damage, it means over two turns you will likely do 5 damage.
How does Toughness affect the math?
The Warhammer Calculator uses the S vs T table: S=T is 4+, S>T is 3+, S>=2T is 2+, S Yes, though AoS uses fixed “To Wound” numbers rather than S vs T comparisons, you can simply adjust the inputs in the Warhammer Calculator to match your unit’s profile. Yes, in the Warhammer Calculator, AP is subtracted from the roll or added to the target number. AP-2 makes a 3+ save into a 5+. Efficiency often comes from the volume of attacks, but high-quality attacks (high AP/Damage) are necessary for “hard” targets according to most Warhammer Calculator simulations. Absolutely not. Understanding the rules and the math of your army is a core part of being a skilled player. Using a Warhammer Calculator helps you learn your army’s capabilities faster.Can I use this for Age of Sigmar?
Does AP reduce the Save roll?
What is the most important stat?
Is Math-hammer considered “cheating”?
Related Tools and Internal Resources